A teacher has two jars of candy on her desk: Jar 1: Contains 3 Strawberry candies and 2 Orange candies. Jar 2: Contains 1 Strawberry candy and 4 Orange candies. The teacher randomly picks two candies from Jar 1 and drops them into Jar 2. Then, a student reaches into Jar 2 and picks two candies . What is the probability that the student picks two Strawberry candies?

Step-by-step solution

Let E₁ be the event that 2 Strawberry candies are transferred from Jar 1 to Jar 2. Let E₂ be the event that 1 Strawberry and 1 Orange candy are transferred. Let E₃ be the event that 2 Orange candies are transferred. Let A be the event that the student picks 2 Strawberry candies from Jar 2. The probabilities of the transfer events are: P(E₁) = ³C₂ ⁵C₂ = 3 10 P(E₂) = ³C₁ ²C₁ ⁵C₂ = 6 10 P(E₃) = ²C₂ ⁵C₂ = 1 10 After the transfer, Jar 2 will contain 7 candies in total. We calculate the conditional probabilities of picki